I'm learning space group, as an exercise, I'm trying to determine all the 14 Bravais lattices by adding base-centered, body-centered or face-centered atom on the simple lattice of 7 crystal family.
But when I'm confronted with hexagonal crystal family, I can't find out why there can't be base-centered, body-centered or face-centered rhombohedral/hexagonal lattice.
Hope someone can show me how to argue there can't be. (for both rhombohedral and hexagonal)
graphics will be of great help!